Subgroups — #17981139

Order 4352.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545842	C₂	1	2	yes	maximal
2	#14543695	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#63241	—	2	2	no	—
4	#11763695	C₄	1	1	yes	characteristic
5	C₈×#3624	C₂²	1	1	yes	characteristic
6	C₁₆×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂×#63241	—	4	2	no	—
8	C₄×#3624	D₄	1	1	yes	characteristic
9	C₄×#3624	Q₈	1	1	yes	characteristic
10	C₂×#63216	—	2	1	no	—
11	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
12	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×#63214	C₈	1	1	yes	characteristic
14	C₂×#3624	—	2	1	no	—
15	C₂×#3624	SD₁₆	1	2	yes	—
16	#63241	—	8	2	no	—
17	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
18	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
19	C₂×#3622	M₁₆	1	1	yes	characteristic
20	#63216	—	2	2	no	—
21	C₁₆×C₁₇	—	2	1	no	—
22	#63214	C₁₆	1	2	yes	complemented
23	#7099	—	17	1	no	maximal, Sylow
24	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
25	C₂×Dic₁₇	#106	1	1	yes	characteristic
26	C₂×Dic₁₇	#108	1	1	yes	characteristic
27	#3624	—	2	2	no	—
28	#3624	—	4	1	no	—
29	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
30	C₈×C₁₇	M₃₂	1	1	yes	characteristic
31	#3622	—	2	1	no	—
32	#1367	—	17	2	no	—
33	#1311	—	17	1	no	—
34	C₂²×C₁₇	#334	1	1	yes	characteristic
35	C₄×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
36	C₄×C₁₇	#364	1	1	yes	characteristic
37	Dic₁₇	—	2	1	no	—
38	Dic₁₇	#365	1	2	yes	—
39	C₄⋊C₁₆	—	34	2	no	—
40	C₄×C₁₆	—	17	1	no	—
41	C₄×C₁₆	—	17	1	no	—
42	C₈²	—	17	1	no	—
43	C₂×C₁₇	#1367	1	1	yes	characteristic
44	C₂×C₁₇	#1368	1	1	yes	characteristic
45	C₂×C₁₇	#1369	1	1	yes	characteristic
46	C₂×C₁₆	—	17	1	no	—
47	C₂×C₁₆	—	34	1	no	—
48	C₂×C₁₆	—	68	2	no	—
49	C₂×C₁₆	#3633	1	1	yes	characteristic
50	C₄×C₈	—	17	1	no	—
51	C₄×C₈	—	17	1	no	—
52	C₄×C₈	—	17	1	no	—
53	C₁₇	#7099	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₈	—	17	2	no	—
55	C₂×C₈	—	17	1	no	—
56	C₂×C₈	—	34	1	no	—
57	C₂×C₈	C₂×#3633	1	1	yes	characteristic
58	C₄²	—	17	1	no	—
59	C₁₆	—	2	1	no	—
60	C₁₆	—	17	2	no	—
61	C₁₆	—	34	2	no	—
62	C₁₆	—	136	2	no	—
63	C₂×C₄	—	17	1	no	—
64	C₂×C₄	—	17	1	no	—
65	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
66	C₈	—	34	2	no	—
67	C₈	—	34	1	no	—
68	C₈	—	68	1	no	—
69	C₈	#10587665	1	1	yes	characteristic
70	C₈	#10587670	1	1	yes	characteristic
71	C₂²	#11763898	1	1	yes	characteristic
72	C₄	—	17	2	no	—
73	C₄	—	34	1	no	—
74	C₄	#11763912	1	1	yes	characteristic
75	C₄	#11763914	1	1	yes	characteristic
76	C₂	#14545843	1	1	yes	characteristic
77	C₂	#14545844	1	1	yes	characteristic
78	C₂	#14545847	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11763898
commutator	C₈×C₁₇	C₂×C₁₆
Frattini	C₂×C₈	C₂×#3633
Fitting	C₂×C₁₆×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	#334
cosocle	C₈×#3624	C₂²
hypercenter	C₂×C₁₆	#3633
hypocenter	C₁₇	#7099
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
22. #63214	C₁₆	semidirect
53. C₁₇	#7099	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14545842	2
#14543695	2
#7099	17